Question: Jazmin is completing an art project. She has two pieces of construction paper. The first piece is $44$ cm wide and the second piece is $33$ cm wide. Jazmin wants to cut the paper into strips that are equal in width and are as wide as possible. How wide should Jazmin cut each strip?
Explanation: In order to know how wide Jazmin should cut each strip, we need a number that is a factor of ${44}$ and ${33}$, so that the piece that is ${44}$ cm wide and the piece that is ${33}$ cm wide can be cut into equal strips. So, if Jazmin cut each piece of paper into strips $\gray{1}$ cm wide, there would be ${44} \div \gray{1} = 44$ strips from the first piece and ${33} \div \gray{1} = 33$ strips from the second piece. This creates strips with the same width, but it sure doesn't give us the greatest width possible! To find the greatest width possible, we want to find the greatest common factor of ${44}$ and ${33}$. To do so, let's find factors of ${44}$ and ${33}$. ${44}$ : $1, 2, 4, {11}, 22, 44$ ${33}$ : $1, 3, {11}, 33$ The greatest common factor of ${44}$ and ${33}$ is ${11}$. In math notation this looks like: $ \text{gcf}({44},{33}) = {11}$. Jazmin should cut each strip ${11}$ cm wide.